Physics 362 – week 4

Modern Physics Seminars

Distances in the solar systemThe movement of the planets is described using celestial

mechanics

F = G mM/r2

Kepler’s laws (P2=k r3)

astronomical unit = average distance of the Earth from the Sun

1 a.u. = 149,598,073 Km

Distances beyond the solar system

Trigonometric parallax

Trigonometric Parallax

1 a.u.

d

d = 1 a.u. / sin a.u.in radiants

Trigonometric parallax

Trigonometric parallax

Trigonometric Parallax

1 a.u.

d

d = 1 a.u. / sin a.u.

Trigonometric parallax

Parsec = distance of a star when the parallax is equal to 1”

d = 1 a.u. / sin a.u.in radiants

1 pc = 1 a.u. / (1” 1 rad) = 206,265 a.u.

1 pc = 3.1 1013 Km = 3.26 light-years

Trigonometric parallax

Closest star: Alpha Centauri is 1.3 pc away

Parallax = 0”.76

Only a small number of stars can be measured!!!

Current accuracy: ~0”.005 dmax~200 pc

Distance scales

Distances beyond 200 pc

Motion of the sun in the galaxyv ~ 30 Km/s ~ 4.1 a.u. / year

In 10 years 41 a.u.

Can be used to measure up to ~ 2000 pc

Distances beyond 200 pc

Calibrated candles!!!

Light intensity: Id = Ie / r2

we can measure Id, and if we know Ie

we can evaluate r

Calibrated candles•Stars from the H-R diagram

•Variable stars

•Type II supernovae

•Galaxies

Spectroscopy

cv

cv

0obs1

1ff

cv

cv

0obs1

1

c

v1

1

1z

cv

cv

0

0obs

redshift

For approaching source

Redshift

Hubble law

v = H · r (H = Hubble constant)

Hubble lawH > 0

The universe is expanding

Earth at the center of the Universe?

NO!

H = v / r ~ 70 km / s / Mpc

H = time-1

vmax = c

Rmax = vmax / H = 6000 Mpc ~ 2 1023 Km = 2 1010 light/years

Hubble lawRewind the film

BIG BANG!!!

Age of the universe:

Objects at distance = R = v / H Time to get this far:

T = R / v = 1 / H ~ 6.2 1017 s ~ 1.5 1010 years (15 Billion years)

Einstein and Hubble• The theory of general relativity predicts a dynamic

universe (either expanding or contracting)

• Einstein didn’t believe in a dynamic universe and modified his theory, introducing an extra term (the vacuum energy density ) in his equations, to have a static universe

• When Hubble published his results Einstein defined his modified theory “the biggest blunder of my life”

• A term similar to has now been reintroduced to explain recent results in Cosmology